AutoX is a time trial type of race so, you won't need a special insurance for it. Besides the moment you tell your insurance agent that you race your car ... your rates will jump 2,3 even 4x as much.
I asked mine a long time ago, and she said don't bring it up again unless I was doing it professionally. It's really costly.
You would need to be doing the hardcore road rally, road race or rally cross to be in a different insurance bracket.